In a regular triangular pyramid SABC, R is the midpoint of the edge AB, S is the vertex.

In a regular triangular pyramid SABC, R is the midpoint of the edge AB, S is the vertex. BC = 4, and the lateral surface area is 36. Find SR.

Since the pyramid is regular, a regular triangle lies at its base, and the areas of its lateral faces are equal.

Then the area of one side face of SAB will be equal to: Ssav = Spir / 3 = 36/3 = 12 cm2.

The side faces are isosceles triangles. Since point R is the midpoint of side BC, then segment SR is the median of triangle SBC, and since it is isosceles, then its height.

Then Ssвс = ВС * SR / 2.

SR = 2 * Ssbc / BC.

Since triangle ABC is correct, AB = BC = 4 cm.

Then: SM = 2 * 12/4 = 6 cm.

Answer: The length of the SR segment is 6 cm.